This paper presents a numerical study and the optimization of very short discrete multi-pump Raman amplifiers using Tellurite-based optical fibers. While most studies about discrete Raman amplifiers usually focus on cases where hundreds of meters of fiber are used, here we consider a multi-pumped Raman amplifier setup with extremely short dimensions, in which the length of the gain media was varied from 2.5 to 30 meters. The optimization process was developed over an broad amplification band from 1520 to 1600 nm, considering a maximum acceptable ripple of 3 dB, and using 2, 3 and 4 pumps with individual powers always below 2.5 W. The results show that it is possible to achieve net gains as high as 10 dB for gain media around 20 meters, and close to 15 dB for 30 meters. These high gains highlight the fact that Tellurite-based optical fibers can be used for the construction of very short and compact broadband amplifiers using just a few pump lasers with modest optical powers.